In measurement and automation technology, the mass flow rate and/or the density of a fluid flowing in a pipe, particularly of a liquid, are frequently determined by means of meters which, using a vibratory transducer and a measuring and control circuit connected thereto, induce reaction forces, particularly Coriolis forces corresponding to the mass flow rate and inertia forces corresponding to the density, in the fluid flowing through the transducer and derive therefrom a measurement signal representing the respective mass flow rate and/or the respective density of the fluid.
Such Coriolis mass flowmeters or Coriolis mass flowmeter-densimeters are disclosed, for example, in WO-A 01/33174, WO-A 00/57141, WO-A 98/07009, U.S. Pat. No. 5,796,011, U.S. Pat. No. 5,731,527, U.S. Pat. No. 4,895,030, U.S. Pat. No. 4,781,069, EP-A 1 001 254, EP-A 553 939, or EP-A 1 154 243. Each of those Coriolis mass flowmeters or Coriolis mass flowmeter-densimeters provides corresponding measurement signals using a vibratory transducer comprising at least one flow tube of predeterminable lumen which serves to conduct a fluid, has an inlet end and an outlet end, is curved at least in segments, and vibrates at least temporarily, and which,                to permit flow of the fluid therethrough, communicates with a connected pipe via an inlet tube section, ending in the inlet end, and an outlet tube section, ending in the outlet end, and        in operation, in order to deform the lumen of the flow tube, performs flexural vibrations about a first axis of vibration, which joins the inlet and outlet ends.        
To generate and maintain the vibrations of the at least one flow tube, each of the transducers is provided with at least one excitation assembly which is energized by the aforementioned measuring and control circuit. The excitation assembly comprises a first, preferably electrodynamic or electromagnetic, vibration exciter, which in operation is traversed by an alternating, particularly bipolar, excitation current and which converts the excitation current into an excitation force acting on the flow tube.
Curved flow tubes, e.g., flow tubes bent into a U- or V-shape in a tube plane, particularly tubes of Coriolis mass flowmeters, are commonly excited in the so-called useful mode into cantilever vibrations so that the flow tubes, undergoing an elastic deformation, will oscillate about the transducer's first axis of vibration. To this end, the vibration exciter is generally positioned in the transducer in such a way as to act on the flow tube at an antinode of the useful mode, particularly at a midpoint region of the tube.
As a result of the cantilever vibrations about the longitudinal axis, Coriolis forces are induced in the fluid, which, in turn, result in cantilever vibrations of the so-called Coriolis mode being superimposed on the excited cantilever vibrations of the useful mode, the cantilever vibrations of the Coriolis mode being equal in frequency to those of the useful mode. In transducers of the kind described, these cantilever vibrations forced by Coriolis forces commonly correspond to torsional vibrations about a second axis of vibration, particularly an axis normal to the first axis, the second axis being essentially parallel to an imaginary vertical axis of the transducer.
With a curved tube shape, thermal expansion will cause practically no or only very slight mechanical stresses in the flow tube itself and/or in the connected pipe, particularly if materials with a high thermal expansion coefficient are used. Furthermore, the flow tube can be made long, particularly with a projecting portion, so that despite a relatively short mounting length, particularly at relatively low excitation power, high sensitivity of the transducer to the mass flow rate to be measured can be achieved.
The aforementioned circumstances also allow the flow tube or flow tubes to be made from materials with a high thermal expansion coefficient and/or a high modulus of elasticity, such as special steel.
The two parallel, essentially identically shaped flow tubes of the transducers disclosed in U.S. Pat. No. 5,796,001 and WO-A 01/33174 are essentially continuously curved, i.e., they are not straight practically anywhere.
By contrast, the flow tubes of the transducers shown in U.S. Pat. No. 5,731,527, U.S. Pat. No. 5,301,557, U.S. Pat. No. 4,895,030, WO-A 00/57141, WO-A 01/33174 or EP-A 1 154 243, for example, each have at least two straight tube segments which are connected via an arcuate tube segment, particularly a circular-arc-shaped segment. Compared to continuously curved flow tubes, such curved flow tubes with straight tube segments have the advantage that they can be manufactured at low cost by means of very simple bending tools. While continuously curved flow tubes generally have projecting arcuate tube segments and in most cases segments with different radii of curvature, flow tubes with straight tube segments can also be made using arcuate tube segments that have a single radius of curvature and/or comparatively small radii of curvature.
Preferably, the flow tubes are vibrated in operation at a natural instantaneous resonance frequency, particularly with the vibration amplitude regulated at a constant value. As the natural resonance frequency is also dependent on the instantaneous density of the fluid, commercially available Coriolis mass flowmeters can also measure the density of moving fluids, for example.
To locally sense vibrations of the flow tube and generate corresponding sensor signals, each of the transducers includes a sensor arrangement comprising at least one inlet-side and at least one outlet-side, e.g., electrodynamic, vibration sensor. Because of the superposition of the useful mode and the Coriolis mode, the vibrations of the flow tube sensed by means of the sensor arrangement on the inlet and outlet sides, and hence the corresponding sensor signals, exhibit a phase difference which is also dependent on the mass flow rate.
By means of the above-mentioned measuring and control circuit, this phase difference can be measured in the manner familiar to those skilled in the art, namely directly or indirectly by determining an amplitude difference, for example, and be used to generate the measurement signal representative of the mass flow rate of the fluid. Furthermore, the measuring and control circuit can determine the density of the fluid by taking into account an instantaneous frequency of at least one of the two sensor signals.
As is well known, in operation, the transducer, particularly the at least one flow tube, besides being subjected to the above-described, desired reaction forces, is also acted on by other physical quantities, particularly by quantities that are not influenceable. For example, due to the thermal expansion of the flow tube, the temperature of the fluid, which in most cases cannot be maintained constant, automatically results in the transducer exhibiting, besides its sensitivity to the primary measurands, i.e., mass flow rate and density, a cross sensitivity to a temperature distribution currently existing in the transducer. To compensate for such temperature-induced perturbing effects on the measurement signals, Coriolis mass flowmeters or Coriolis mass flowmeter-densimeters commonly also incorporate at least one temperature sensor for measuring the temperature of the flow tube or of the environment about the tube, for example.
It is also known that such vibratory transducers, besides having the above-described sensitivity to a spatial and temporal temperature distribution existing inside the transducer, may exhibit a significant cross sensitivity to a static internal pressure existing in the lumen of the flow tube or to a pressure difference existing between the lumen and the environment of the tube. This fact is pointed out also in U.S. Pat. No. 5,731,527, U.S. Pat. No. 5,301,557, WO-A 95/16897, and WO-A 98/07009, for example. Such cross sensitivities can be accounted for by the fact that depending on the level of the internal pressure or on the magnitude of the pressure difference, the fluid counteracts the deformation of the vibrating flow tube with differently great forces.
Unfortunately, such cross sensitivities of the transducer to pressure may result in, mostly undesired, cross talks from pressure to mass flow corresponding Coriolis forces. To ensure the required high measurement accuracy, which generally should be at least within about ±0.15% of the actual mass flow rate or the actual density, additional measures are therefore necessary to compensate for the pressure dependence of the measurement signals, particularly if the internal pressure may vary over a wide range of, e.g., more than 5 bars.
To solve the problem, U.S. Pat. No. 5,301,557, for example, proposes to use flow tubes of comparatively great wall thickness in order to oppose the elastic deformations of the respective flow tube with a force which may be very high but is virtually constant. This, however, particularly because of the resulting increase in the mass of the flow tube, results in the transducer's sensitivity to the primary measurands, i.e., mass flow rate and density, being reduced along with the cross sensitivity to pressure. U.S. Pat. No. 5,731,527 proposes a similar solution in which the straight tube segments are provided with tubular stiffening elements of anisotropic, particularly glass-fiber-reinforced, materials, which stiffening elements serve to impart to the straight tube segments stiffnesses dependent on the orientation of the mechanical stresses acting in the respective tube segments, thus making the flow tube more pressure-resistant While maintaining good sensitivity to Coriolis forces.
Another possibility of reducing the transducer's cross sensitivity to pressure is described in WO-A 98/07009 or WO-A 95/16897. It is proposed to determine the internal pressure or the pressure difference during operation by means of resonance frequencies of two different, simultaneously or successively excited vibration modes of the at least one vibrating flow tube, and to take this internal pressure or pressure difference into account in the generation of the measurement signal representing the mass flow rate. To this end, the excitation assembly disclosed therein has, in addition to the usual single exciter, at least a second vibration exciter, which acts on the flow tube at a given distance from the first exciter. As is readily apparent, this involves an additional amount of mechanical complexity as well as a considerable additional amount of complexity of the measuring and control circuit, in which additional arithmetic capability must be provided. On the one hand, this substantially increases the manufacturing costs of such a Coriolis mass flowmeter-densimeter. On the other hand, such an increase in the complexity of both the installed hardware and the firmware implemented therein entails a disproportionate increase in error probability or even in the probability of failure and, thus, a substantial increase in the complexity of the monitoring necessary to ensure the required reliability of the Coriolis mass flowmeter-densimeter.